Euro-Bund Futures Exploratory Data Analysis by Alessandro Landi

This dataset is a financial time series of Bund futures, i.e. the futures contract on the 10yr bond issued by the German government. A futures contract is the commitment to buy or sell some given underlying product at a certain date.

The dataset starts on 12th May 2016 and ends on 29th Sep 2017. It is a subset of a proprietary dataset belonging to the independent quantitative trading research project FQT Research, whose owners kindly agreed to be used for the scope of this project. It contains a few missing dates due to some server-side connection issues in some occasional circumstance.

Each row is a snapshot taken every 5 minutes of:

• the bid price
• the ask price
• the daily cumulative bid volume
• the daily cumulative ask volume
• the cumulative bid volume of the trades larger than 100 contracts
• the cumulative ask volume of the trades larger than 100 contracts

Some notes for the sake of clarification:

• the bid price is the price at which a market participant sells a financial security
• the ask price is the price at which a market participant buys a financial security
• the bid price is usually lower and never higher than the ask price and the ask price is usually higher and never lower than the bid price, because the brokers earn from the spread, therefore when we buy we buy higher and when sell we sell lower
• the bid volume is the number of contracts that were traded by the initiative of a seller who met the offer a buyer
• the ask volume is the number of contracts that were traded by the initiative of a buyer who met the offer a seller

The dataset

## Summary of the entire dataset:

##       bid             ask             bidv             askv       
##  Min.   :158.8   Min.   :158.8   Min.   :     0   Min.   :     1  
##  1st Qu.:161.6   1st Qu.:161.6   1st Qu.: 82751   1st Qu.: 83774  
##  Median :163.2   Median :163.2   Median :178627   Median :179510  
##  Mean   :163.0   Mean   :163.0   Mean   :187335   Mean   :187771  
##  3rd Qu.:164.3   3rd Qu.:164.3   3rd Qu.:275860   3rd Qu.:276468  
##  Max.   :168.5   Max.   :168.5   Max.   :656814   Max.   :641295  
##  hundreds_bidv    hundreds_askv   
##  Min.   :     0   Min.   :     0  
##  1st Qu.: 23402   1st Qu.: 23887  
##  Median : 53558   Median : 53812  
##  Mean   : 58247   Mean   : 58438  
##  3rd Qu.: 87036   3rd Qu.: 88012  
##  Max.   :231872   Max.   :215364

About this particular dataset, it is key to understand that, for the sake of our analysis, bid and ask are uniquely used to compute the mid price by averaging them. Then, we are not even so much interested in the mid price itself, but rather in its first derivative with respect to a change in time, which we compute below. The reason is that we are more interested in the change in price rather than in the price itself.

All other values are cumulative volume values. Therefore, they represent a snapshot of the cumulative value at each time of the day. For the limited scope of this specific, we have chosen to not investigate the differences between bid volume and ask volume. We have chosen to just focus on the overall volume by simply summing the two. Again, we are not interested in the volume data per se but rather in its first derivative with respect to a change in time.

We have chosen limit the focus of our analysis to the following three key features:

• volatility (change in price)
• liquidity (change in volume)
• proportion of large trades vs. overall trades (change in trades whose size is larger than 99 over change in overall volume)

More detail on their computation will be provided below.

Univariate Plots Section

## Summary of changes in price over 5-min intervals (in absolute value):

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00    0.01    0.02    0.02    0.03    0.95

In order to measure the volatility of the price, we computed the differentials between the price at time t and the price a time t + 5 minutes. Then we took the absolute value of the differentials we cause in this case we are more interested in how much the price moved rather than its direction. We can see that the range is very wide, ranging from 0 to 0.95.

## Summary of changes in price over 5-min intervals (in absolute value)
## below 99th centile:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00000 0.01000 0.02000 0.02286 0.03000 0.11500

This is the same summary but here, for the sake of better insight of what happens in the usual case, we removed all data points beyond the 99th centile. From here we can see that in 99% of the cases the price oscillation is between 0 and 0.115. This implies that occasionally there are some exceptionally large outliers between 0.115 and 0.95.

## Summary of changes in total volume over 5-min intervals:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0     837    2998    3674    5184   79099

This summary gives an idea of the 5-min liquidity. By liquidity we mean the number of contracts traded among market participants. We can see that again the range of values is quite wide and goes from 0 to 79099.

## Summary of changes in total volume over 5-min intervals
## below 99th centile:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     0.0   816.8  2961.0  3476.9  5097.0 16421.0

As we did for the volatility summary, again for the sake of better insight of what happens in the usual case, we removed all data points beyond the 99th centile. From here we can see that in 99% of the cases the number of traded contracts is between 0 and 16421. This implies that occasionally there are some exceptionally large outliers, like we saw when we measured the volatility.

## Summary of changes in total volume greater than 99 contracts
## over 5-min intervals:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0     100     732    1135    1642   23489

Here we are measuring the number of traded contracts whose minimum trade size was greater than 99. It is worth to point out at each trade has a trade size and a market participant can choose to trade either one contract at time or many contracts at once. Only large traders such as banks, hedge funds or exceptionally wealthy individuals have the capacity to trade more than one hundred contracts at once. Therefore, this reveals the presence of large traders. However, it is not sufficient to reveal the extent of their presence, as nothing prevents these traders to trade small quantities as well. Nonetheless, it is a measure of the lower bound of such extent.

## Summary of changes in total volume greater than 99 contracts
## over 5-min intervals, below 99th centile:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0     100     716    1058    1604    6408

Same as above, again for the sake of better insight of what happens in the usual case, we removed all data points beyond the 99th centile. From here we can see that in 99% of the cases the number of traded contracts is between 0 and 6408 This implies that occasionally there are some exceptionally large outliers, like we saw when analyzing previous variables as well.

This plot shows the distribution of the liquidity over 5-min intervals. We can see that the mode is in the first bin, between 0 and 200. This is likely to be due to the fact that many of these 5-min interval happen at times when the market is open but there is little activity. The vertical line in the middle represents the median of the distribution, while the dashed lines represent respectively the 10th, 25th, 75th and 90th centile.

This plot shows the distribution of the subset of the liquidity where the trade size was larger than 99 contracts over 5-min intervals. It may appear reasonable for the data to have this shape because - as we pointed out earlier - these are the trades made by large traders. Since it takes a lot of financial capacity to make these trades, it appears reasonable that the most frequent observations are the lowest and the least frequent ones are the highest. Like the previous plot, the vertical line in the middle represents the median of the distribution, while the dashed lines represent respectively the 10th, 25th, 75th and 90th centile.

This plot shows the distribution of price movements over 5-minute intervals. In this case, we are not looking at the asbolute value because we interested in seeing there is any skew in the distribution. From this plot, we can see that the distribution appears quite symmetrical to the naked eye, so that it seems appropriate to infer that there are approximately as many positive and negative prices changes. This also appears to legimitize the choice of looking at the absolute value of changes in price, since taking the sign away does not appear to cause a substantial loss of information.

Univariate Analysis

## 'data.frame':    51787 obs. of  9 variables:
##  $ bid            : num  164 164 164 164 164 ...
##  $ ask            : num  164 164 164 164 164 ...
##  $ bidv           : num  0 435 1318 2737 3481 ...
##  $ askv           : num  433 1145 1690 2523 3156 ...
##  $ hundreds_bidv  : num  0 0 109 239 239 470 470 569 569 669 ...
##  $ hundreds_askv  : num  433 543 543 543 543 ...
##  $ mid            : num  164 164 164 164 164 ...
##  $ totalv         : num  433 1580 3008 5260 6637 ...
##  $ hundreds_totalv: num  433 543 652 782 782 ...

## 'data.frame':    51475 obs. of  3 variables:
##  $ mid            : num  0.015 -0.03 -0.02 0.01 0.01 ...
##  $ totalv         : num  1147 1428 2252 1377 881 ...
##  $ hundreds_totalv: num  110 109 130 0 231 120 199 114 227 0 ...

Bivariate Plots Section

This plot aims at verifying the hypothesis we considered in the paragraph above. It shows the distribution of volume (totalv) by hour of day. The vertical line in the middle represents the median of the distribution, while the dashed lines represent respectively the 10th, 25th, 75th and 90th centile. It is important to clarify that the centiles refer to the plot of the overall unsplit distribution. Its purpose is to make how the distribution of each hour is similar or different than the general one. Indeed this plot confirms the hypothesis we confirmed in the last paragraph: after 18, the distribution becomes very positively skewed and it such a way that it affects the overall distribution.

This scatterplot shows the liquidity by hour of day. The dashed lines represent respectively the 10th and the 90th centile, while the line in the middle represent the median by hour. From here we can see a reasonable pattern:

• a peak at the opening of the London Stock Exchange and the majority of other European exchanges at 9:00 CET
• a progressive decrease until European lunch-time
• another peak at 14:30 and 15:30, i.e. one hour before the opening of the New York Stock Exchange and at its open
• a final peak at 17:30, when the London Stock Exchange and the majority of other European exchanges close and intraday traders need to close their intraday positions.

This plot represents the price changes every 5 minutes in absolute terms, i.e. irrespective of their direction. It measures the volatility of the price over 5-minute intervals.

We can see a few spikes:

• at the opening of the EUREX Exchange at 8:00 CET
• at the opening of the London Stock Exchange and the majority of other European exchanges at 9:00 CET, until 10:00
• between 14:30 and 15:00, i.e. one hour before the opening of the New York Stock Exchange
• between 15:30 and 17:30, i.e. during the morning session of the New York Stock Exchange

We can also see a clear decrease in volatility after 17:30, when the London Stock Exchange and most European markets close.

Given price changes are expressed in absolute terms, of course there is a lower bound at zero. The median is at 0.02 most of the time, with a few spikes at 0.03 and 0.04 in the time ranges mentioned above and then it goes to 0.01 after London and other European markets close. It is interesting to notice approximately 90% of the price moves are below 0.07, yet approximately 1 in 10 moves is above that threshold, with some very significant outliers not appearing in this plot only for the sake of better readability.

## Correlation between liquidity and volatility:

## 0.5269955

We may argue there might be a slight correlation between liquidity (totalv) and volatility (abs(mid)), as we can see that when liquidity becomes high it is rarer too observe low volatility and when volatility becomes high it is rarer too observe low liquidity. As a result, the shape of our jitter plot has a diagonal tendency, but we may arguably find it a little bit too foggy to confidently believe in a reliable correlation as there are too many cases liquidity is relatively high and volatility is relatively low and viceversa.

## # A tibble: 5 x 4
##     weekday absmid_median absmid_75th_centile absmid_90th_centile
##      <fctr>         <dbl>               <dbl>               <dbl>
## 1    Monday         0.015                0.03                0.05
## 2   Tuesday         0.020                0.03                0.05
## 3 Wednesday         0.020                0.03                0.05
## 4  Thursday         0.020                0.04                0.06
## 5    Friday         0.020                0.03                0.06

This boxplot shows the 5-min volatility by weekday:

• Of course, given we express it in absolute terms, the min is at zero for all days
• The 25th centile is at .01 for all days
• The median is at .02 for all days expect Monday, slightly lower al .015
• The 75th centile is at .03 for all days expect Thursday, which is the most volatile day at .04
• The 90th centile is at .05 from Monday to Wednesday and .06 on Thursday and Friday.

It is interesting to notice that Friday’s 90th centile is at .06 like Thursday’s while its 75th is at .03 like Monday to Wednesday’s. This may suggest lower volatility in the more usual case but higher in the lower part of the extremes.

It is also interesting to notice 1 in 100 observations is above .12 and can go as far as .95, which is a quite wild move for a 5-minute interval. This means that - on average - every hundred 5-min intervals, we have one swing ranging between .12 and .95. One in hundred 5-min intervals means one every 500 minutes, i.e. one every 8.33 hours approximately. Given the EUREX Exchange is open 14 hours per day (from 8 to 22), this suggests we may expect these moves 1.7 times per day. This might arguably appear to be too frequent to be ignored.

This plot represents only those points whose absolute mid value was above the 99th centile, i.e. all those points we did not consider in the boxplot showing the 5-min volatility by weekday. As much as we consider that choice legitimate for the sake of its specific purpose, it appears worth noting - as we suspected above and as it is confirmed by this plot - these points appear too frequent to be ignored. By watching this plot to the naked eye, one might be tempted to set the threshold above .25 and below -.25 in order to consider these points true outliers.

Yet, for the sake of keeping correct perspective, it is also useful to keep in mind that the bulk of observations is within -.1 and .1, as it is shown by this plot of all observations with an alpha of .1.

Bivariate Analysis

Multivariate Plots Section

## # A tibble: 5 x 5
##     weekday totalv_25th_centile totalv_median totalv_75th_centile
##      <fctr>               <dbl>         <dbl>               <dbl>
## 1    Monday              602.00          2463             4284.75
## 2   Tuesday              876.00          3098             5245.00
## 3 Wednesday             1044.00          3259             5521.00
## 4  Thursday              945.00          3414             5790.00
## 5    Friday              752.25          2882             4960.50
## # ... with 1 more variables: totalv_90th_centile <dbl>

## geom_path: Each group consists of only one observation. Do you need to
## adjust the group aesthetic?

This plot shows that we have an upward trend in liquidity from Monday to Thursday and then it subsides on Friday. The median volume of each day is respectively 2463, 3098, 3259, 3414, 2882.

This plot represents the price changes every 5 minutes in absolute terms, i.e. irrespective of their direction, by direction of price movement, ‘up’ when the change in price is positive and ‘down’ when it is negative. The behavior appears to be quite similar. There are a few differences here and there but they appear to be negligible. This seems to confirm the symmetrical distribution of price changes that we observed earlier.

This is the same plot as above but with an additional split by day of week. We can see that here and there it is possible to notice a few differences on a day-by-day, yet it is not very intuitive to spot them.

## Summary of median change in price by hour of day and day of week:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00000 0.01000 0.02000 0.01897 0.02000 0.05000

This 3D surface aims at uncovering patterns in a more intuitive way. It shows the median volatility of the price as a function of day of week and time of day. It is red when volatility is high (or metaphorically hot) and blue when it is low (or metaphorically cold).

This heatmap aims at showing the same as above, but it seems to us that it shows outcome in a even more visually clear way.

## Summary of median change in volume by hour of day and day of week:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    76.0   815.6  3574.2  3135.9  4755.1  9163.0

This 3D surface shows the median liquidity a function of day of week and time of day. Again, it is red when volatility is high (or metaphorically hot) and blue when it is low (or metaphorically cold).

This heatmap aims at showing the same as above, but it seems to us that it shows outcome in a even more visually clear way.

## Summary of median proportion of large trades vs overall volume
## by hour of day and day of week:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.1082  0.2812  0.2133  0.3150  0.3847

Multivariate Analysis

Final Plots and Summary

Reflection

The thing that required most attention was clarifying what I wanted to do. I noticed that until I have not well clarified what I want to visualize, any attempt is a struggle. On the other hand, after careful reflection of what it is that we want to see, it becomes much easier to obtain it. In particular, the heatmaps required some thought in order to clarify that for each (time, weekday) couple we needed to reduce all the points their median and use the long or wide form based on whether we were using plotly’s 3D surface or ggplot2’s heatmap.

What was surprising to me what how clearly the patterns of liquidity and volatility emerged and how clear this difference is when some markets are open or not. In particular, we have seen that despite the fact that the EUREX Exchange is open between 8:00 and 22:00, most of the activity in terms of liquidity and volatility happens between 9:00 and 17:30, i.e. the times when the London Stock Exchange is open. It was interesting to notice that activity fades after 17:30 despite the fact that the New York Stock Exchange is open until 22:00 CET.

Further exploration of the data might include doing the same heatmaps only between 9:00 and 17:30, i.e. only when the London Stock Exchange and most other European exchanges are open, under the assumption that the ‘real’ trading day is between 9:00 and 17:30. Therefore, it may be interesting to re-assess what is high, medium or low level of liquidity, volatility or other features in that subset of the data which is constituted by what we have arguably named the ‘real’ trading day. Moreover, a trader might want to do a heatmap of the performance of their model as a function of time of day and day of week and compare it to the heatmaps of liquidity, volatility and other features, in order to obtain a visual intuition of whether its model performs better or worse when the features have take a certain value range.